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Snow-covered mountains are one of the most beautiful sights in nature, but in the wrong circumstances they can kill you. Skiers and other mountain enthusiasts sometimes refer to avalanches as the “white death”, and for good reason. Hundreds die in avalanches every year, and a great deal of effort is spent on trying to understand the factors that cause avalanches in the hope of decreasing this toll.

Located in the Alps and a mecca for winter sports, Switzerland takes avalanches seriously. The Swiss Institute for Snow and Avalanche Research (SLF) monitors snow conditions, issues warnings, and collects data on avalanches. Their web site is very interesting for those interested in winter sports in the Alps. I find the snow maps particularly useful. But for this post I will use their data on fatal Swiss avalanches in the last 20 years to experiment with different ways to visualize some patterns and relationships.

The dataset includes information on the date, location, elevation, and number of fatalities, in addition to the slope aspect, type of activity involved (e.g. off-piste skiing), and danger level at the time of the avalanche. Over the last 20 years there have been 361 fatal avalanches in Switzerland, for a total of 465 deaths. Most avalanches killed only one victim.

Because I wanted to experiment with radial plots, I’ll focus on the variable of slope aspect in this post. Aspect is the compass direction that a slope faces. In this case we’re looking at the slope where the avalanche occurred. In Switzerland, the majority of avalanches occur slopes facing NW – NE, as you can see from this plot:

The gaps at NNE and NNW are probably artifacts of how the aspect data was reported.

This pattern is common in the temperate latitudes of the northern hemisphere. Avalanches are more common on north-facing slopes because they are more shaded and therefore colder, which allows snowfall to remain unconsolidated for longer. When more snow falls, these unconsolidated layers can act as planes of weakness on which snow above can slide. It’s much more complicated that that, with factors like wind and frost layers coming into play. To learn more about how aspect and avalanches, see here. The pattern is unmistakable, but does it hold all year long? I separated the data by month to find out:

Fatal avalanches occurred in all months, but are much more common December – April

A few interesting insights emerge from this plot. First, February is clearly the most deadly month for avalanches. In December there are actually quite a few avalanches on SE facing slopes, but by January the predominate direction is centered around NW. In February, and to some extent in March, it changes to N-NE. In April it’s NW again, but by then there are significantly few avalanches. So there are some monthly patterns, but I’m not exactly sure what the explanation is. Of course to really nail this down we’d want to do some statistics as well.

One pattern I expected, but did not see, was a decrease in the dominance of northern aspects later in the spring. I expected this because as the days get longer, the shading effect of north facing slopes decreases. It’s important to remember that these are fatal avalanches, and a dataset of all avalanches would look different. For example there are probably a lot of wet avalanches on southern slopes in the spring. But these are much less dangerous than the slab and dry powder avalanches, and therefore not reflected in the fatality data.

The rose style plots above are useful, but I wanted to try to illustrate more variables at once. So I tried a radial scatter plot:

Click on the image for the interactive Plot.ly version

This plot is similar to the previous ones in that the angular axis represent compass direction (e.g. 90 degrees means an east-facing slope). The radial axis (the distance form the center) represent the elevation where the avalanche occurred. And color represents the type of activity that resulted in the fatality or fatalities. Each point is one avalanche. The data are jittered (random variations in aspect) to minimize overplotting. This is necessary because the aspect data are recorded by compass direction (e.g. NE or ESE). The density of the points clearly illustrates the dominance of north-facing aspects. It’s also clear that most avalanches occur between 2000 and 3000 meters (in fact the mean is 2507 m). In terms of activity, backcountry touring and off-piste skiing and boarding dominate. And avalanches at very high altitudes are mostly associated with backcountry touring, which makes sense, as not many lifts go up above 3000m. Perhaps especially perceptive viewer can make out some other patterns in the relationships between variables, but I can’t. Any thoughts on the usefulness of this plot for the dataset?

Finally, I want to share a couple graphics from SLF (available here). Here is a timeline of avalanche fatalities in Switzerland since 1936:

The average number of deaths per year is 25, but this has decreased a bit in the 20 years. There were also more deaths in buildings and transportation routes prior to about 1985. Presumably improvements in avalanche control and warnings reduced fatalities in those areas. And what happened in the 1950/51 season. That was the infamous Winter of Terror. The next plot shows the distribution of fatalities by the warning level in place when the avalanche occurred:

Interestingly, the great majority of deaths happened when warning levels where moderate or considerable. There were significantly fewer deaths during high or very high warning periods. One reason must be that high/very high warnings don’t occur that frequently, but it’s also likely that skiers and mountaineers exercise greater caution or even stay off the mountain during these exceptionally dangerous times. There’s probably some risk compensation going on here. To really quantify risk, you have to know more than just the number of deaths at a given time or place. You also have to know how many people engaged in activities in avalanche country without dying. One clever approach is to use social media to estimate activity levels, as demonstrated in this paper.

A while back I was thinking about European colonialism and the enormous impact it’s had on world history. Wouldn’t it be nice to have a simple visualization to illustrate colonization and decolonization around the world? It occurred to me that a dumbbell dot plot would work well for this task. Here’s what I came up with:

The chart shows the dates of colonization and independence of 100 current nations. The countries are organized into broad regions (Asia, Africa, and the Americas), and sorted by date of independence. Color represents the principal colonial power, generally the occupier for the greatest amount of time.

There are many interesting patterns visible in the chart. For example, you can clearly see Spain’s rapid conquest of Central and South America, and then even more rapid loss of its colonies in the 1820s. The scramble for Africa in the late 19th century stands out well, as does the rapid decolonization phase of the late 1950s through early 1970s.

About the Data

To reduce complexity to a manageable level, I set some limitations on what countries to include. First, the chart shows only those countries victim to Western European colonialism. I don’t include Ottoman, Japanese, Russian, American, or other colonial empires. I also don’t include territories that are still governed by former colonial powers (e.g. Gibraltar). This gets controversial and complicated. Countries that were uninhabited upon discovery by colonial powers are also not included. The same with countries that later gained independence from a post-colonial state (e.g. South Sudan).

The dates of independence come from the CIA World Factbook (here). Dates of colonization were derived by my own research, mostly from Wikipedia country pages. I quickly found that establishing a date of colonization is a somewhat subjective decision. Do you choose the date of first European contact? Formal incorporation of the territory into the colonial empire? For the most part, I chose the date of the first permanent European settlement. Notes on the rationale for the date chosen are include in the data spreadsheet (below). In looking at the chart, it’s important to remember that in many cases colonial subjugation was a long process, moving from initial contact, to trade, conquest, settlement, and incorporation.

Constructing the Plot

I wanted to make this plot using ggplot2 in R, but was not sure about best approach. So I reached out on Twitter to dataviz guru and dot plot enthusiast @evergreendata

A quick note on color: I choose colors from the flags of the principal colonial powers to represent them on the plot (except for the Netherlands for which I picked orange). The idea is to make it easier for the viewer to match the color with the country without having to always go back to the legend. I’d be interested in any reactions to this approach. In general, I’d be thrilled with any feedback on how to make this plot better.

I just saw a trailer for the movie San Andreas. It looks preposterous but I love geology disaster movies, so I’ll probably see it. In the film, a series of earthquakes destroy California, culminating with a giant magnitude 9.5 quake. Fortunately the Rock is on scene to help save the day.

The largest earthquake ever recorded in real life struck central Chile on May 22, 1960. With a magnitude of 9.6 (some estimates say 9.5) this was a truly massive quake, more than twice as powerful as the next largest (Alaska 1964), and 500 times more powerful than the April 2015 Nepal quake. The seismic energy released by the 1960 Chile quake was equal to about 20,000 Hiroshima atomic bombs. Thousands were killed. It also triggered a tsumami that traveled 17,000 km across the Pacific Ocean and killed hundreds in Japan.

But I think the most striking thing about this quake is that it accounts for about 30% of the total seismic energy released on earth during the last 100 years. To illustrate this, I calculated the seismic moment (a measure of the energy released by an earthquake) of all earthquakes greater than magnitude 6 and plotted the global cumulative seismic moment over the last 100 years.

Click for interactive version

This plot clearly shows how the 1960 Chile quake (and to a lesser extent the 1964 Alaska event) dominates the last 100 years in terms of total energy released. This is not always obvious as the earthquake magnitude scale is logarithmic. So a magnitude 9.6 releases twice as much energy as a 9.4 and 250 times as much as an 8.0.

Technical notes: To make this plot I downloaded from the USGS archive data on all the earthquakes greater than magnitude 6 from 1915-2015. There are about 10,500 of them.

I calculated the seismic moment for each quake relative to a magnitude 6 (the smallest in the database) using

Where m1 is the magnitude of each quake and m2 = 6.

So a mag 9.6 is about 250,000 times more powerful than a mag 6.0. (Note that this refers to energy released, not necessarily ground shaking, which is influenced by many factors, such as earthquake depth).

Then I summed all the relative moments, normalized to 1, and plotted the cumulative seismic moment over the time period.

A few caveats. First, the quality of the magnitude measurements has improved over time, so that the data from the earlier part of the 20th century is not as reliable as the more current data.

Second, this analysis only looks at earthquakes larger than magnitude 6.0. Of course there are many, many smaller earthquakes. However, the cumulative amount of seismic energy released by these smaller quakes is very small compared to the larger ones (again, remember the logarithmic scale).

Third, the magnitudes listed in the USGS archive are calculated in different ways. The majority are moment magnitude or weighted moment magnitude. The equation above is meant for these types of magnitude. Other magnitude measurements, such as surface wave magnitude, have slightly different ways of calculating total energy release. This may introduce some inaccuracies, However, they will be small compared relative to total energy release.

If any seismologists would like to weigh in, I would be most grateful.

More information on calculating magnitude and seismic moment here and here.

You’re probably familiar with the concept of population density. It’s the total population divided by the area. When talking about cities, it’s commonly understood that high population density is a necessary if not sufficient condition for urban vibrancy and efficient mass transit. But it can be difficult to compare population densities of metropolitan areas because the administrative boundaries have an arbitrary effect on measurement. For example, if the LA metro area is defined at the county level and includes all of San Bernardino County, which is mostly empty desert, you get a pretty meaningless density measurement.

Now, you can look at smaller administrative areas to get a better handle on the population density of a city. In the U.S. the census tract is the highest resolution. With the areas and populations of each census tract, you can calculate an even more interesting metric: population-weighted density, which is the the average of each resident’s census tract density. That means that areas where more people live get more weight in the overall density calculation.

Another way to think about population-weighted density is the density at which the average person lives. The simple population density of the entire U.S. is 87 people per square mile. That really does not tell us much. But the population-weighted density is over 5,000 people per square mile. The average American lives in an urban area. (That example is from a U.S. Census report on metropolitan areas.)

An interesting (if not intuitive) insight from population-weighted density is the strong relationship between city size and density. Big cities are more dense. The plot below shows the population weighted densities and total populations of the 100 U.S. largest cities (well, technically core-based statistical areas). Click on the image for the interaction version if you want to mouse over the dots to identify individual cities.

Click for interactive version. Note log-log scale.

The cities are categorized by region, showing the general pattern that southern cities are the least dense and northeastern and western cities the most dense. This regional difference is emphasized in the linear fits shown for each region. I was surprised by how dense on average the western cities are. Honolulu is a real outlier in terms of having a high density for its size. Unsurprisingly, the sprawling giants of Atlanta, Dallas, and Houston are low-density outliers.

Incidentally, I got the idea for this graph after listening to a very interesting podcast on Streetsblog about the urban form of Milwaukee. It mentioned that Milwaukee is actually one most the most dense cities for its size, especially when looking in the Midwest. And sure enough, Milwaukee lies well above the blue trend line for Midwest cities. If you have 45 minutes and are interested in Milwaukee you should definitely listen to the podcast. Full disclosure: I was born and raised there.

Technical notes: Plot made with plot.ly using data from U.S. Census. The color palette is inspired by the film Rushmore and is from Karthik Ram’s wesanderson R package. Yes, this was all an elaborate excuse to try out the Wes Anderson color palettes.

A nice in-depth look at urban density and implications for transit can be found here.

Finally, if you are interested in extreme urban density, check this out. I can’t vouch for the accuracy of the data, but the web site name suggests it’s probably pretty legit.

It’s been quite some time since my last post. I have been busy with a young child, new job, and an international move. But I’m hoping to get back into posting and making visualizations on a regular basis.

The reason for this post is that I came across an interesting resource called the International Environmental Agreements Database Project, hosted at the University of Oregon. The database contains information on about 1100 multilateral environmental agreements (MEAs) dating back to 1857. The data include the title, type (an original agreement or a protocol or amendment to an existing agreement), dates of signature and entry into force, and the parties. For some agreements there is even data on performance as well as coding to allow for comparison of the actual legal components.

As an initial exploration, I simply looked at how many agreements were concluded over time. The plot below shows the results for the last 100 years. Click for the interactive and shareable plot.ly version.

Click for interactive version

There is a pretty interesting pattern. From the early 20th century until the 1950s there are not that many MEAs. Then the pace picks up in mid-century, peaking in the early 1990s, and declining considerably after that.

The Earth Summit was a huge event in the global environmental community, and occurred at a high point of optimism about multilateralism. There was a flurry of MEA activity around this time. But there was also a building movement to ensure that international environmental diplomacy was benefiting the poor, and in particular, developing countries.

The Rio Declaration enshrined the principle of common but differentiated responsibilities. This is the idea that while all nations have a responsibility to protect the global environment, rich nations should shoulder a greater share of the burden.

It is a noble sentiment, and one that in my view makes a lot of sense. But it had the effect of making it more difficult to reach agreements in international environmental negotiations. Developing countries started going into the negotiations expecting more support, in the form of funding, reduced obligations, or technology transfer, from the developed world. Common but differentiated responsibilities is at the root of a major sticking point in global climate talks. Should China, India, and other rapidly developing nations have the same stringent obligations as more mature economies?

I certainly don’t think this is the only cause of the decline in new MEAs in the last 20 years. And neither can I claim to be the first to think about the Rio Declaration’s impact on MEAs. There’s an entire literature on it. For example, Richard Benedick discussed this theme at length in reference to the Montreal Protocol and its aftermath in his book Ozone Diplomacy.

As a final disclaimer, for this analysis it would be best to filter the IEA database to exclude those MEAs that only have a few parties. That way you could really focus on the rate of global or large regional MEAs over time. Perhaps I’ll do that next.

But in any case, it’s an interesting dataset and an interesting pattern. And a good excuse to step back and think about the big picture in global environmental politics.

Recently there has been bit of buzz about a study claiming that female named hurricanes cause more fatalities, on average, than male ones. The authors suggested that the discrepancy is attributable to gender bias. Female named hurricanes do not seem as threatening to people, so presumably they take fewer precautions. From the start this seemed pretty far-fetched, and in fact a number of problems have been found with the study.

But it got me thinking about hurricane names. A more likely effect of a hurricane’s name would be to discourage parents from giving their children that name, if the hurricane is associated with death and destruction. Fortunately, there is readily available data with which to test this hypothesis. For hurricanes, I used the same data as the hurricane gender study described above (they may have had some problems with their methodology, but at least they released their data). It contains data on 92 Atlantic hurricanes that made landfall in the U.S. since 1950*. For baby names I turned to the Social Security Administration. There is a great R package called babynames that makes the yearly SSA data available in a readily accessible format for use in R. As an aside, the SSA baby names data is the source of all sorts of interesting visualizations and analyses, such as the baby name voyager and this article from fivethirtyeight.com on predicting a person’s age based on their name.

The tricky part of this analysis is deciding how to define a decrease in name usage after a hurricane. The simplest way would be to look at how many times a name was given in the year of a hurricane versus how many times that name was given the following year. For example, how many baby Kartrinas were there in 2005 versus 2006. However, this method does not take into account that most names are either decreasing or increasing in popularity as part of a longer-term trend. So you have to look at how the popularity of a name was changing before the hurricane as well. To see why, look at this plot of the number of babies named Katrina over time.

Katrina peeked in popularity in in 1980 and has been declining ever since. But from 2004-2005 the number of Katrina’s actually increased about 13%. From 2005-2006, however, it decreased dramatically – by 26%. It’s a pretty good bet that this rapid decrease was due to the hurricane.

To quantify the change in a name’s usage after a hurricane, I made the assumption that the best predictor of how a name’s popularity will change in a given year is how it changed last year. To calculate the post-hurricane change in name usage I subtracted the percent change in name usage in the year before the hurricane from the percent change after the hurricane. In the Katrina example the post hurricane change would be (-26%) – (13%) = -39%. This post-hurricane percent change value is what I use in the analysis below.

Before we get to the results, let’s take at look at the fascinating case of Carla:

Hurricane Carla was an extremely intense storm that hit Texan in 1961, killing 43. The name “Carla” had been surging in popularity, but after 1961 it started a decline in popularity from which it never recovered. It seems a pretty good bet that the hurricane had a major role in Carla’s decline. Interestingly, the first live television broadcast of a hurricane was of Carla, with a young Dan Rather himself reporting from Galveston. Could the shock of the American TV-viewing public seeing footage of the storm in their living rooms have contributed to the demise of Carla as a name?

Back to the analysis. Indeed, the hurricane baby name effect seems real. After running the numbers, I found that names associated with a landfalling hurricane were about 15 percent less common in the year after the hurricane. Out of the 93 hurricanes in the data set, 65 were associated with a decrease in the popularity of their names, and only 21 were followed by increasing name usage. (Seven hurricane names were not found in the SSA data in their landfall year).

So far this is pretty intuitive. Of course people are less likely to name their dear infant after a natural disaster. Based on this reasoning, you’d expect that the more fatalities caused by a hurricane, the greater the baby name effect. Let’s test that.

The effect is quite small. When we take Katrina out (a massive outlier in terms of fatalities), it’s smaller still:

So the correlation between change in baby name usage and hurricane fatalities is quite weak. Finally, I had to see if the gender of the hurricane name affected this relationship. Were more deadly female-named hurricanes more or less likely than male names to affect baby name popularity? Maybe I’d even find that male baby name usage goes up with hurricane fatalities because parents associate the names with strength? I can see the Slate headline now! Alas, there is no significant difference:

By the way, there are more female names because from 1950 – 1979 all Atlantic hurricanes were given female names.

There’s an almost endless amount of interesting things to glean from the baby names data. My ultimate dream is an algorithm to determine the perfect name for your baby based on a number of criteria chosen by the expectant parents. It would really take the stress out of the naming process. One of the criteria would certainly be that the name is not on the World Meteorological Association’s list of tropical storm names!

This post is intended to illustrate the cool things you can do with plot.ly’s API for R. Plot.ly is a web-based tool for making interactive graphs. It uses the D3.js visualization library, and lets you create very attractive plots that can be easily shared or embedded in a web page. With the R API you can manipulate data in R and then send it over to plot.ly to create an interactive graph. There’s also a function that let’s you create a plot in R using ggplot2, and then shoot the result directly over to plot.ly (summarized nicely here).

I have great little free app on my iPhone called Pedometer++ that keeps track of how many steps I take each day. I exported the data, plotted up a time series with ggplot2, and used the API to make the graph in plot.ly. It worked quite nicely. The only hiccup was that plot.ly did not recognize the local regression curve, so I had to add that separately.

You can see from the plot that I’m not consistently meeting my 10,000 step goal. In fact, I averaged 7,002 steps over this period. That still comes out to a total of 1,470,463 steps. From October through February my step count was trending slightly downward, but since then it’s picked up. Maybe that had something to do with the cold winter. Hopefully as the weather (and my motivation) improves, I’ll hit my goal.

Click to see the interactive version

Any here’s a bonus box plot showing steps taken by day of the week (also using the R API):

Click to see the interactive version

If there are any pedometer users out there who are interested, let me know and I can post the code.

One of the first posts on this blog was about using Tableau to visualize data on global emissions of mercury. I’ve gotten suggestions from a few people and given the graphic a bit of a face lift. Click on the image to see the interactive viz:

Click for interactive graphic

I also used the same dataset to make some static graphics using ggplot2 and the ggthemes package. I’d love any input on how to improve the the look and feel of both these and the Tableau viz. I’ve always found picking good colors very challenging, so thoughts on the palettes are especially welcome.

The 8 industry sectors with the highest global mercury emissions. Data for 2010 from the 2013 UNEP Global Mercury Assessment.

Countries with the highest mercury emissions. Data for 2010 from the 2013 UNEP Global Mercury Assessment.

A while ago I wrote a post suggesting that Ukraine’s propensity for revolution might have something to do with its high level of government corruption in combination with its relatively well-developed civil society. As evidence for this, I showed that Ukraine (together with Kyrgyzstan and Moldova, two countries that have also recently experienced political unrest) was an outlier among post-Soviet states with respect to the relationship between corruption perceptions and authoritarianism. This finding was interesting, but by no means robust enough to warrant broad generalizations about corruption and democracy and revolution.

Since then, a few others chimed in with some ideas. Ben Jones suggested looking at corruption and authoritarianism in countries that experienced revolutions over time. Cavendish McCay looked at corruption and authoritarianism data from the same sources but over the entire globe, and produced a very cool visualization. He also pointed me to the World Bank’s Worldwide Governance Indicators, which contains measures of democracy, corruption, and political stability. Perhaps it would be possible to test my hypothesis empirically using these data. This could be done for individual regions or for the whole world, and could also have a temporal component (the indicators have been published since 1996).

In order to determine if such an analysis is feasible, I decided to take a closer look at the dataset (which is free and downloadable from the website). The Worldwide Governance Indicators (WGI) project is an ambitious one. The authors compile data from 31 different sources (such as think tanks, NGOs, private firms) and produce annual scores for every country for six indicators of the quality of governance. The indicators are:

Voice and Accountability

Political Stability and Absence of Violence

Government Effectiveness

Regulatory Quality

Rule of Law

Control of Corruption

First off, we can look at the data on a map. Fortunately the WGI website has a series of nice Tableau interactive graphics, including maps:

Looking at the indicators geographically is helpful. But to evaluate whether they can be used to test the hypothesis, I want to see how each indicator is correlated with all the others. For this, we’ll turn to R. Here is a correlation matrix of the six indicators as calculated for 2012. Positive correlations are reflected as positive values. The closer the the number to one, the stronger the correlation. As you can see, all the indicators are positively correlated to each other, some very strongly. This is not surprising. We would expect well-governed countries to get high marks for rule of law, regulatory quality, control of corruption, etc. One interesting observation here is that Control of Corruption actually has the lowest correlations of all the indicators. A scatter plot matrix is a good way to look at the data in more detail:

The idea for this variation on the scatter plot matrix comes from Winston Chang’s R Graphics Cookbook. Its structure is similar to the correlation matrix in that all of the indicators are plotted against each other. The lower panels show scatter plots with LOESS regression lines for each indicator pair. This plot has some extra bells and whistles thrown in – histograms of the distribution of each in indicator in the diagonal panels and correlation coefficients (just like the correlation matrix) in the upper panels. The scatter plots show the strong to moderate correlations that we already saw in the correlation matrix, but allow us to make out some curious features of the data, like the non-linear relationship between Voice and Accountability and many of the other indicators.

The indicator values are in units of a standard normal distribution. A value of zero is the mean, while a value of one is one standard deviation higher than the mean. Given the distributions, the indicator values range from about -2.5 to 2.5. Positive values represent better governance, negative represent worse. Because each indicator is measured on the same scale, we can simply sum all six to determine the overall “best governed” country. The top six are:

I got a bit carried away examining the correlations between the governance indicators, but in a subsequent post I hope to look closer at the democracy – corruption – stability hypothesis. I’m still not quite sure what statistical tests to use and how to apply them, and I’d welcome any ideas. Data and code are posted on Github (github.com/caluchko/wgi)

In the previous post, I used Tableau Public to create a visualization of the Seafood Hg Database. That graphic showed the mean mercury content and number of samples by seafood category. But there are several other dimensions in the database, including the year of the study and the particular species of seafood sampled. I couldn’t resist playing around with the data a little more, this time using the lattice package in R.

The plot below shows the mean mercury concentration (y-axis) in studies of the 12 seafood categories with the highest median mercury concentration. The x axis shows the date of the study. I’ve also plotted a trend line for each panel. This is a nice way to visualize the data, but I wouldn’t read too much into this plot. For one thing, many of the seafood categories contain multiple species, some of which are higher than others in mercury. Also, this plot does not account for the geographical region where the fish were sampled.

We can tease a little more from the dataset by looking at the individual species within a seafood category. Here is a plot of the six tuna species with the greatest number of studies. The larger species, like bluefin, seem have higher mercury contents than the smaller ones, like skipjack. One curious feature of the dataset is also visible here: there were very few studies of mercury in seafood in the 1980s.